diff --git a/sklearn/calibration.py b/sklearn/calibration.py
index 600be8d603da7..b563cdee143cb 100644
--- a/sklearn/calibration.py
+++ b/sklearn/calibration.py
@@ -14,6 +14,7 @@
 from math import log
 import numpy as np
 
+from scipy.special import expit
 from scipy.special import xlogy
 from scipy.optimize import fmin_bfgs
 from sklearn.preprocessing import LabelEncoder
@@ -442,8 +443,7 @@ def _sigmoid_calibration(df, y, sample_weight=None):
 
     def objective(AB):
         # From Platt (beginning of Section 2.2)
-        E = np.exp(AB[0] * F + AB[1])
-        P = 1. / (1. + E)
+        P = expit(-(AB[0] * F + AB[1]))
         loss = -(xlogy(T, P) + xlogy(T1, 1. - P))
         if sample_weight is not None:
             return (sample_weight * loss).sum()
@@ -517,7 +517,7 @@ def predict(self, T):
             The predicted data.
         """
         T = column_or_1d(T)
-        return 1. / (1. + np.exp(self.a_ * T + self.b_))
+        return expit(-(self.a_ * T + self.b_))
 
 
 def calibration_curve(y_true, y_prob, normalize=False, n_bins=5):